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This research paper deals with a numerical algorithm based on the RCW method to solve a set of first-order ordinary differential equations. In this algorithm, the answer of each equation is considered as a polynomial of degree 2. The coefficients used in this polynomial are categorized into groups of free and fixed coefficients. The free coefficients are obtained by optimizing the error function, while the fixed coefficients are computed from the magnitudes of derivative of this polynomial at initial value. To check the correctness of the current algorithm, its results for several case problems are compared with the findings of the Runge-Kutta (RK) method. This comparison shows that the algorithm presented in this paper has a higher accuracy and stability than the RK method even for the nonlinear problems.

A NUMERICAL ALGORITHM BASED ON THE RCW METHOD TO SOLVE A SET OF FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS